1. No category

Linear relationship and the sample correlation coefficient Below
are four bivariate data sets and the scatter plot for each. (Note that
each scatter plot is displayed on the same scale.) Each data set is
made up of sample values drawn from a population.
1. x & y
x 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
y 7.7 7.0 8.0 5.8 6.6 4.4 4.7 3.1 4.1 3.5
u & v ( u - 1-10)
v 6.5 9.2 4.0 9.5 5.1 1.6 5.6 10.1 5.1 8.0
w & t ( w - 1 - 10)
t 3.2 4.7 3.7 5.2 4.4 6.8 5.8 7.9 6.9 8.1
m & n (m - 1-10)
n 3.8 6.0 7.1 4.5 5.0 8.2 5.5 7.2 9.0 7.6
Answer the following questions about the relationships between
pairs of variables and the values of r, the sample correlation
coefficient. The same response may be the correct answer for more
than one question.
Which data set indicates the strongest negative linear relationship
between its two variables?
x&y
For which data set is the sample correlation coefficient r equal to 1?
Is this supposed to say “closest” to -1?
None of them are exactly -1.
x & y is the closest to -1
For which data set is the sample correlation coefficient r closest to
0?
u&v
For which data set is the sample correlation coefficient r closest to
1?
w&t
x
y
1
2
3
4
5
6
7
8
9
10
55
r=
7.7
7
8
5.8
6.6
4.4
4.7
3.1
4.1
3.5
54.9
!
(" xy) # (" x)(" y )
$
'$
'
&%n (" x ) # (" x ) )( &%n (" y ) # (" y ) )(
2
!
2
2
10(257.9) " (55)(54.9)
[10(385) " (55) ][10(329.61) " (54.9) ]
r = "0.9131
!
7.7
14
24
23.2
33
26.4
32.9
24.8
36.9
35
257.9
n
2
r=
x2
xy
2
2
1
4
9
16
25
36
49
64
81
100
385
y2
59.29
49
64
33.64
43.56
19.36
22.09
9.61
16.81
12.25
329.61
u
v
1
2
3
4
5
6
7
8
9
10
55
r=
6.5
9.2
4
9.5
5.1
1.6
5.6
10.1
5.1
8
64.7
!
(" uv ) # (" u)("v)
$
'$
'
&%n (" u ) # (" u) )( &%n (" v ) # (" v ) )(
2
!
2
2
10( 355.9) " (55)(64.7)
[10(385) " (55) ][10(485.09) " (64.7) ]
r = 0.000675
!
6.5
18.4
12
38
25.5
9.6
39.2
80.8
45.9
80
355.9
n
2
r=
u2
uv
2
2
1
4
9
16
25
36
49
64
81
100
385
v2
42.25
84.64
16
90.25
26.01
2.56
31.36
102.01
26.01
64
485.09
w
t
1
2
3
4
5
6
7
8
9
10
55
r=
3.2
4.7
3.7
5.2
4.4
6.8
5.8
7.9
6.9
8.1
56.7
!
(" wt) # (" w)(" t)
$
'$
'
&%n (" w ) # (" w ) )( &%n (" t ) # (" t ) )(
2
!
2
2
10( 354.2) " (55)(56.7)
[10(385) " (55) ][10(347.93) " (56.7) ]
r = 0.90675
!
3.2
9.4
11.1
20.8
22
40.8
40.6
63.2
62.1
81
354.2
n
2
r=
w2
wt
2
2
1
4
9
16
25
36
49
64
81
100
385
t2
10.24
22.09
13.69
27.04
19.36
46.24
33.64
62.41
47.61
65.61
347.93
m
n
1
2
3
4
5
6
7
8
9
10
55
r=
3.8
6
7.1
4.5
5
8.2
5.5
7.2
9
7.6
63.9
!
(" mn) # (" m)(" n)
$
'$
'
n
m #
m
n
n #
n
%& (" ) (" ) () %& (" ) (" ) ()
2
!
2
2
10( 382.4 ) " (55)(63.9)
[10(385) " (55) ][10(434.19) " (63.9) ]
r = 0.66995
!
3.8
12
21.3
18
25
49.2
38.5
57.6
81
76
382.4
n
2
r=
m2
mn
2
2
1
4
9
16
25
36
49
64
81
100
385
n2
14.44
36
50.41
20.25
25
67.24
30.25
51.84
81
57.76
434.19